On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was cycling with the the wind and subtracted 3 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 48 miles with the wind, he could only go 30 miles against the wind. What is his normal bicycling speed with no wind?

Question

Jasmin

Mathematics

27 September, 09:56

On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was cycling with the the wind and subtracted 3 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 48 miles with the wind, he could only go 30 miles against the wind. What is his normal bicycling speed with no wind?

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Fiona Clark · Answer 1

13 mph

using d=rt you can set up 2 equations

48 = (r+3) t

30 = (r-3) t

solving these both for t and setting them equal warrants

48 / (r+3) = 30 / (r-3)

and with cross multiplication and distribution you get

48r-144=30r+90

solving for r you get r=13